It is implied there were more than one vampire clan in Skyrim. Twice! One mentioned in Immortal Blood, explained by Huleed. And this:
In my previous volume of notes and observations regarding http://www.uesp.net/wiki/Skyrim:Dimhollow_Crypt's possible connections to the ancient http://www.uesp.net/wiki/Skyrim:Vampire clans of http://www.uesp.net/wiki/Lore:Skyrim's history, I wrote of a great chamber, far larger than anything else I've yet seen here in the crypt.
Notice the plural. Clans!
Also, Harkon and his family are pureblooded vampires, yes, but they aren't the only pureblooded vampires. Lamae Beolfag is a pureblood and she preceeed Harkon's family. Hell, even a "Cyrodiilic" vampire could be pureblooded. They know their history, they honor Lamae Beolfag and even mentioned her in the book. I am sure in their elitist personality, some might of been pureblooded as well.
As far as the Order goes, we know little about this clan. What information we have from them is that they are a secret fraternity, strict, and they worship Molag Bal and Clavicus Vile, possibly even making pacts and rituals with Molag Bal as one of those vampires compares the Bat to a "brother".
Anyone can be pureblooded. It is said the Daughters of Coldharbour are made by a ritual we all know about, but it is tradition among vampires, therefore known. Of course, it is a ritual not that many people survive.
Also. we cannot go calling the vanilla vampires "Order" just because they might be Cyrodiilic vampires. It is like calling thin-blooded" vampires Volkihar, even though they are not part of the clan. Order Vampyrum is
the clan of Cyrodiil, and the members are all composed of individuals who have influence; Nobles, counts, politicians, aristocrats, etc. Most of the named vampired NPC's fit these descriptions and even the Order's nature.
Seridur is manipulative and deceitful, seductive when it comes to other men's women, he sends the player out to kill other vampires. He is a good member of society.
Jakben Earl of Imbel is a nobleman, who prowls the night feeding on people in the city. He has an unblemished reputation in the city.
Janus Hassildor hates barbaric vampires, whom he might consider "thin-blooded". He's a count, rich and wealthy, and everyone in the city never had a problem with him.
Lord Lovidicus, nobleman, wealthy, rich. Surrounded by servants, one of whom he fell in love with. His journal explains how much of a civil man he is.
Being "Order" means being part of the clan, and being part of the clan, the individual has to have a good power base, and has to follow the tenets(though many of these guys were a bit hypocritical when it came to revealing themselves). The vampires we find dwelling in caves and forts, howling and screaming in Oblivion are not Order. They're savage thin-blooded creatures, who are not kin. The Volkihar share the same exact sentiment, as do some of the vampires in Morrowind.